MANAGING REPAIRABLE SUPPLIES USING MARKOV CHAINS

This paper aims to present a mathematical approach to managing repairable supplies by employing discrete-time Markov chains with finite state spaces. Repairable items, such as aircraft spare parts and industrial machinery, for example, are frequently used in the world due to their potential for reuse. However, determining the optimal turnover quantity for such items is a very complex task. This study proposes modeling the shortage variable, obtained from historical demand and return data, as a Markovian stochastic process. Using Gaussian smoothing, a transition matrix was constructed, and the state vector represents the system's state changes over time. Some simulations using real-world data demonstrate the model’s accuracy and practicality. This approach is both mathematically intuitive and computationally efficient, offering a robust and efficient tool for inventory optimization in repairable supply chains. Suggestions for further research include exploring matrix’s spectral gap analysis and the use of continuous-time Markov models with variable probabilities.